abc is a triangle i which altitudes bd and ce to sides ac and ab are equal (i) ∆abd is congruent to ∆ace (ii) ab=ac i.e abc is an isosceles triangle
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Given: ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal.
To prove: In ΔADB and ΔACE
Proof: ∠ADB=∠AEC=90 degree (altitudes BD and CE to sides AC and AB)
BD=CE (Given altitudes are equal)
∠BAD=∠CAE (Common angle )
ΔABD≅ΔACE [by AAS congruence]
So AB=AC (by CPCT)
∴ triangle ABC is an isosceles triangle.
Step-by-step explanation:
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